Edexcel IGCSE 2009

Specification and Sample Assessment Material Edexcel International GCSE in Mathematics (Specification A) (4MA0) First examination 2011

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Authorised by Martin Stretton Prepared by Parul Patel Publications code: UG022527 All the material in this publication is copyright © Pearson Education Limited 2012

International GCSE Mathematics (Specification A) (4MA0)

Specification

First examination 2011

Introduction The Edexcel International General Certificate of Secondary Education (International GCSE) in Mathematics (Specification A) is designed for use in schools and colleges. It is part of a suite of International GCSE qualifications offered by Edexcel.

Key subject aims The Edexcel International GCSE in Mathematics (Specification A) qualification enables students to: 

develop their knowledge and understanding of mathematical concepts and techniques



acquire a foundation of mathematical skills for further study in the subject or related areas



enjoy using and applying mathematical techniques and concepts, and become confident to use mathematics to solve problems



appreciate the importance of mathematics in society, employment and study.

About this specification Key features and benefits of the specification The Edexcel International GCSE in Mathematics (Specification A) has been developed to focus on: 

tiers of entry that allow students to be entered for the appropriate level



questions designed to be accessible to students of all abilities within that tier



papers that are balanced for topics and difficulty



standards that are equivalent to Edexcel’s UK GCSE in Mathematics



a full range of teacher support



a solid basis for students wishing to progress to Edexcel AS and Advanced GCE Level, or equivalent qualifications.

Contents Specification at a glance

1

External assessment

2

Calculators

3

Qualification content

5

Knowledge, skills and understanding

5

Papers 1F and 2F (Foundation Tier)

7

Papers 3H and 4H (Higher Tier)

Assessment

21

31

Assessment summary

31

Assessment Objectives and weightings

31

Relationship of Assessment Objectives to Papers for International GCSE

32

Entering your students for assessment

32

Student entry

32

Combinations of entry

32

Access arrangements and special requirements

32

Assessing your students

33

Awarding and reporting

33

Language of assessment

33

Malpractice and plagiarism

33

Student recruitment

34

Progression

34

Grade descriptions

34

Support and training

37

Edexcel support services

37

Training

37

Appendices

39

Appendix 1: Suggested resources

41

Appendix 2: Formulae sheet for Foundation Tier

43

Appendix 3: Formulae sheet for Higher Tier

45

Specification at a glance This Edexcel International GCSE qualification is comprised of two externally assessed papers. Students are entered at either Foundation Tier or Higher Tier. Foundation Tier students will take papers 1F and 2F. Questions in the Foundation Tier paper are targeted at grades in the range C – G. The highest grade which will be awarded at Foundation Tier is grade C. Higher Tier students will take Papers 3H and 4H. Questions in the Higher Tier paper are targeted at grades in the range A*– D. There is a ‘safety net’ grade E for students who narrowly fail to achieve grade D. Students who fail to achieve grade G on Foundation Tier or grade E on Higher Tier will be awarded Ungraded. Foundation Tier 

Externally assessed



Availability: January and June series



First assessment: June 2011



Two papers: 1F and 2F

Paper code: 4MA0/1F and 4MA0/2F Each paper is 50% of the total International GCSE marks

Overview of content 

Number



Algebra



Geometry



Statistics

Overview of assessment 

Each paper is assessed through a two-hour examination set and marked by Edexcel.



The total number of marks for each paper is 100.



Each paper will have approximately equal marks available for each of the targeted grades.



Each paper will assess the full range of targeted grades at Foundation Tier.



There will be some common questions targeted at grades C and D, across papers 1F and 3H and papers 2F and 4H, to aid standardisation and comparability of award between tiers.

UG022527 – Specification – Edexcel International GCSE in Mathematics (Specification A) (4MA0) – Issue 1 – March 2012 © Pearson Education Limited 2012

1

Higher Tier

Paper code: 4MA0/3H and 4MA0/4H



Externally assessed



Availability: January and June series



First assessment: June 2011



Two papers: 3H and 4H

Each paper is 50% of the total International GCSE marks

Overview of content 

Number



Algebra



Geometry



Statistics

Overview of assessment 







Each paper will have approximately equal marks available for each of the targeted grades.



Each paper will assess the full range of targeted grades at Higher Tier.



Questions will assume knowledge from the Foundation Tier subject content.



There will be some common questions targeted at grades C and D, across papers 3H and 1F and papers 4H and 2F, to aid standardisation and comparability of award between tiers.

External assessment In all examination papers: 

diagrams will not necessarily be drawn to scale and measurements should not be taken from diagrams unless instructions to this effect are given



each student may be required to use mathematical instruments, eg pair of compasses, ruler, protractor



calculators may be used



tracing paper may be used



formulae sheets will be provided.

2


Calculators Students will be expected to have access to a suitable electronic calculator for all examination papers. The electronic calculator to be used by students attempting Foundation Tier examination papers (1F and 2F) should have these functions as a minimum: 

1

+, , , , x 2, x, memory, brackets, xy, x y , sine, cosine, tangent and their inverses.

The electronic calculator to be used by students attempting Higher Tier examination papers (3H and 4H) should have these functions as a minimum: 

1

+, , , , x 2, x, memory, constant function, brackets, xy, x y , x , x, fx, standard form, sine, cosine, tangent and their inverses.

Calculators with any of the following facilities are prohibited in all examinations: 

databanks; retrieval of text or formulae; QWERTY keyboards; built-in symbolic algebra manipulations; symbolic differentiation or integration.


3

4


Qualification content Knowledge, skills and understanding This Edexcel International GCSE in Mathematics (Specification A) requires students to demonstrate application and understanding of the following. Number 

Use numerical skills in a purely mathematical way and in real-life situations.

Algebra 

Use letters as equivalent to numbers and as variables.



Understand the distinction between expressions, equations and formulae.



Use algebra to set up and solve problems.



Demonstrate manipulative skills.



Construct and use graphs.

Geometry 

Use properties of angles.



Understand a range of transformations.



Work within the metric system.



Understand ideas of space and shape.



Use ruler, compasses and protractor appropriately.

Statistics 

Understand basic ideas of statistical averages.



Use a range of statistical techniques.



Use basic ideas of probability.


5

6


Papers 1F and 2F (Foundation Tier) Content overview 

Number –







Numbers and the number system

Algebra –

Equations, formulae and identities

–

Sequences, functions and graphs

Geometry –

Shape, space and measure

–

Vectors and transformation geometry

Statistics

Assessment overview 

Two written papers.









Each paper weighted at 50% of the qualification, targeted at grades C – G.


7

Content AO1 Number and algebra 1

Numbers and the number system Students should be taught to:

1.1 Integers

Notes

understand and use integers (positive, negative and zero) both as positions and translations on a number line understand place value use directed numbers in practical situations

To include temperature, sea level

order integers use the four rules of addition, subtraction, multiplication and division use brackets and the hierarchy of operations use the terms odd, even and prime numbers, factors and multiples identify prime factors, common factors and common multiples 1.2 Fractions

understand and use equivalent fractions, simplifying a fraction by cancelling common factors

8 60

 152 in its simplest

form (lowest terms)

understand and use mixed numbers and vulgar fractions identify common denominators apply common denominators to order fractions calculate a given fraction of a given quantity, expressing the answer as a fraction express a given number as a fraction of another number use common denominators to add and subtract fractions convert a fraction to a decimal or a percentage

understand and use unit fractions as multiplicative inverses

3 5

= 0.6 = 60%

4 9

= 0.4444… = 0. 4

35=3

.

1 5

multiply and divide a given fraction by an integer, by a unit fraction and by a general fraction

8


1.3 Decimals

use decimal notation order decimals

1.4 Powers and roots

convert a decimal to a fraction or a percentage

Terminating decimals only

recognise that a terminating decimal is a fraction

0.65 =

65 100



13 20

identify square numbers and cube numbers calculate squares, square roots, cubes and cube roots use index notation and index laws for multiplication and division of positive integer powers express integers as the product of powers of prime factors

1.5 Set language and notation 1.6 Percentages

720 = 24  32  5

understand the definition of a set use the set notation ,  and  and  understand the concept of the Universal Set and the Empty Set and the symbols for these sets

= Universal Set Ø or { } = Empty Set

understand that ‘percentage’ means ‘number of parts per 100’ express a given number as a percentage of another number express a percentage as a fraction and as a decimal understand the multiplicative nature of percentages as operators

15% of 120 = 15  120 100

solve simple percentage problems, including percentage increase and decrease

Find the interest earned after one year on £3,000 invested at 5% per annum Find 100% when another percentage is given

1.7 Ratio and proportion

use ratio notation, including reduction to its simplest form and its various links to fraction notation

Expressing in the form 1: n

divide a quantity in a given ratio or ratios

Share £416 in the ratio 5:3 or 4:3:1

use the process of proportionality to evaluate unknown quantities calculate an unknown quantity from quantities that vary in direct proportion

s varies directly as t. Find the missing value in a table

solve word problems about ratio and proportion

Including maps and scale diagrams


9

1.8

Degree of accuracy

round integers to a given power of 10 round to a given number of significant figures or decimal places identify upper and lower bounds where values are given to a degree of accuracy use estimation to evaluate approximations to numerical calculations

By rounding each value to one significant figure, estimate the value of 4.9  24.6 to one 46.3

significant figure 1.9

Standard form

1.10 Applying number

Higher Tier only. use and apply number in everyday personal, domestic or community life carry out calculations using standard units of mass, length, area, volume and capacity

Metric units only

understand and carry out calculations using time carry out calculations using money, including converting between currencies 1.11 Electronic calculators

10

use a scientific electronic calculator to determine numerical results.

3.32 +  4.3 correct to 2 significant figures


2

Equations, formulae and identities Students should be taught to:

2.1 Use of symbols

Notes

understand that symbols may be used to represent numbers in equations or variables in expressions and formulae understand that algebraic expressions follow the generalised rules of arithmetic use index notation for positive integer powers

a3 = a  a  a

use index laws in simple cases

x3  x2 = x5 x

7

x

3

x

4

3

(x )  x 2

2.2 Algebraic manipulation

x

2

x

5



6

1 x3

evaluate expressions by substituting numerical values for letters collect like terms multiply a single term over a bracket take out single common factors

Factorise x2 + 3x

expand the product of two simple linear expressions

(x + 3)(x  2) = x2 + 3x  2x  6 = x2 + x  6

2.3 Expressions and formulae

understand that a letter may represent an unknown number or a variable use correct notational conventions for algebraic expressions and formulae substitute positive and negative integers, decimals and fractions for words and letters in expressions and formulae

Evaluate 2x  3y when x = 2 and y=4

use formulae from mathematics and other real-life contexts expressed initially in words or diagrammatic form and convert to letters and symbols


11

2.4 Linear equations

solve linear equations, with integer or fractional coefficients, in one unknown in which the unknown appears on either side or both sides of the equation

3x + 7 = 22 2 3

x = 60

4x – 2 = 10  x 5x + 17 = 3(x + 6) 15  x =2 4 1 6

set up simple linear equations from given data

x+

1 3

x=5

The three angles of a triangle are a, (a + 10), (a + 20). Find the value of a

2.5 Proportion

Higher Tier only.

2.6 Simultaneous linear equations

calculate the exact solution of two simple simultaneous equations in two unknowns

2.7 Quadratic equations

Higher Tier only.

2.8 Inequalities

understand and use the symbols >,

Edexcel IGCSE 2009

Edexcel IGCSE 2009

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